It is important to fully realize the importance of cubism. It isn't just "Picasso's style" but marks the real beginning of abstract art. Picasso's predecessors, such as the impressionists, the fauvists and Cezanne were still principally tied to nature as a model to elaborate on. With Les Demoiselles d'Avignon Picasso reached a level of abstraction that was a radical enough break with the classical dominance of content over form, a hierarchy which is reversed in Les Demoiselles d'Avignon and the style which followed from it: Cubism.

Cubism as a forth dimension explained quickly... I suppose not really a 4th spacial dimension, but a concept that is carried through the 4D experience; being able to see all sides, and insides of everything, all at once.

Carl Sagan has gone bunkers, and discusses dimensionality. Gets good only after he stops discussing flatland, after about 5 minutes... but still, a nice review of it in classic Sagan speak.